Hunting for Exoplanet Moons

by Paul Gilster on October 23, 2008

We’re all interested in transiting planets smaller than the Neptune-sized Gliese 436b, and sure to find many of them as our methods improve. One day soon, via missions like COROT or the upcoming Kepler, we’ll be studying planets close to Earth mass and speculating on conditions there. But here’s a scenario for you: Suppose the first Earth-mass detection isn’t of a planet at all, but a moon orbiting a much larger planet? That challenging scenario comes from David Kipping (University College London) in a new paper on the detection of such moons.

I should be calling them ‘exomoons,’ the satellites of planets around other stars. It’s reasonable enough to assume they’re out there in the billions given the nature of our own Solar System. And compared to the multitude of giant planets found thus far, an Earth-mass exomoon in the habitable zone would seem to offer a far more benign environment for life. The trick, of course, is to pull off a detection, for most exomoons are going to be smaller than the Earth. Varying orbital distances will make the moon hard to spot during a transit, at times hiding the moon behind or in front of the planet. But Kipping notes that variations in the time a planet takes to transit its star could be one clue to the presence of such a moon.

It’s an interesting thought, but does it tell us enough? The transit timing variation (TTV) signal varies according to both the mass of the exomoon and its orbital separation from the planet it circles. It becomes impossible using transit timing variations alone to determine the mass of the exomoon without plugging in some value for its orbital separation. It’s a conundrum unless a secondary method can be found that works in conjunction with transit timing variations to tease out the exomoon’s parameters. Kipping finds that method in transit duration variation (TDV), which offers a signal of the same magnitude, and one that can be larger than TTV itself.

Measure multiple transits over a period of time and periodic changes in its duration are what make up the TDV value. In a recent email, Kipping said this about the relationship between TTV and TDV:

The moon and planet both orbit a common centre of mass, albeit a position very close to the planet’s centre. The effect of this is that the planet seems to wobble… As you can see, not only the position, but the velocity of the planet is shifting constantly. The spatial wobble causes TTV and the velocity wobble causes TDV. Hence, you will see why they must be 90 degrees out of phase!

Here is an animation of the process (all effects greatly exaggerated for clarity):

I send you to the paper for the relevant equations, but using them Kipping is able to show that transit duration variation allows us to measure the moon’s mass without making assumptions about its orbital separation. It then becomes possible to derive the orbital period itself. A hypothetical planet identical to GJ 436b, for example, but with a 35.7 day period in a circular orbit would be in the habitable zone of the star it circles. An Earth-mass exomoon around such a world would be an achievable target. Studies of GJ 436b show that such a transit timing variation signal would be well within reach of existing instruments. From the paper:

This suggests that the detection of the exomoon should be presently possible through TTV from the ground and feasible with TDV in the near future. This illustrates that even ground-based instruments could detect an Earth-like body in the habitable zone using timing effects.

All of which points to data future observers should be gathering:

We also ﬁnd that current ground-based telescopes could detect a 1 [Earth mass] exomoon in the habitable zone around a Neptune-like exoplanet. The author would therefore encourage observers to produce not only their mid-transit times, but also transit durations for each transit, rather than composite lightcurve durations. This will allow constraints to be placed on the presence of exomoons around such planets.

The science of exomoons takes us yet deeper into understanding exoplanetary systems. Not only am I jazzed about the scientific implications here, but I’m reminded to ask readers for recommendations on science fiction treatments of habitable moons around gas giants. Who knows what settings may become imaginable as we begin the detection of such moons through planetary transits? The paper is Kipping, “Transit Timing Effects due to an Exomoon,” accepted by Monthly Notices of the Royal Astronomical Society and available online.

Addendum: The original paper on using transit timing variations to detect exomoons is Sartoretti and Schneider, “On the detection of satellites of extrasolar planets with the method of transits,” Astronomy and Astrophysics Supplementary Series 134 (1999), pp. 553-560 (abstract). In an email, Dr. Schneider notes that the COROT team had already begun searching for TTV signatures before the appearance of Dr. Kipping’s paper. It will be interesting to see how TTV and TDV play out in the analysis of any resulting data.

I’m reminded to ask readers for recommendations on science fiction treatments of habitable moons around gas giants. Who knows what settings may become imaginable as we begin the detection of such moons through planetary transits…

“The Alabama has entered the 47 Ursae Majoris system and is approaching the third planet, Bear. Bear is huge and one of its six moons is larger even than Mars. This moon has been named Coyote, and is lush with green plants and rivers of water…”

Whether 47 Ursae Majoris is an actual system with planets and moons is another story.

How about Robert Heinlein’s Universe story from the 1930s,
which was later turned into Orphans of the Sky, probably the
most famous of all the stories about a group of humans living
on a multigenerational starship and not knowing it.

The protagonists end up living on an Earth-type moon around
a Jovian type exoplanet.

“For extrasolar systems, this research suggests that the largest satellites of a Jupiter-mass planet would be Moon-to-Mars sized, so that Jovian-sized exoplanets would not be expected to host satellites as large as the Earth. This is relevant to the potential habitability of satellites in extrasolar systems.”

However a mars sized moon and a Jupiter sized planet, in the habitable zone of a star could still be a nice habitable target to look for.

How big would a planet have to be to have an earth sized moon around it?

If the ratio is indeed .0001 for the mass of all moons in a gas giant system, and the max around 1J = 1M, then X x J = 10m … x = 10 x Jupiter mass (miniumum)(mars 1/10 mass of earth … I think). If the calcs are correct we might not find any earth sized planets around anything smaller than a brown dwarf … which is still ok …

Most of the action in “The Algebraist”. by Iain M. Banks, occurs on the moons and in the atmosphere of a gas giant, where the moons are inhabited by human colonists, and the planet Nasqueron itself by the Gas-Giant Dwellers. It’s probably one of the couple of best science fiction books written this decade, and displays Banks’ usual far-reaching talent and Copernican space opera style.

In the 1983 Star Wars VI film, Return of the Jedi, Endor, the Forest
Moon that the Death Star II orbits was supposedly once circling
a gas giant planet until the planet was destroyed. But the moon
was somehow left unaffected, thankfully for the Ewoks.

a quick scan of the Extrasolar Planets Encyclopedia showed me that of the 294 extrasolar planets in the main table, some 50 are of at least 1 Jupiter mass (up to 18 Mj) at between 0.7 and 1.5 AU semi-major axis, orbiting a roughly sunlike star (from F6 – K2, main sequence V and subgiant IV; excluding a few M dwarfs and KIII giants).

That means that just over 1 in 6 extrasolar planets discovered so far is a giant planet (>= 1Mj) roughly in or near the habitable zone.

There’s some signs that Titan and Triton were both captured into orbits around their primaries and Uranus was knocked over by a large impactor – that sounds like they were initially Trojans perturbed into walking orbits. Evidence – i.e. lack of a hyperbolic excess – also suggests Theia formed as a Trojan before its perturbation and collision with Earth. Some open questions – did a Trojan strip Mercury of its mantle? Was Mars a Jupiter Trojan? How easy can Trojans be captured?

To me this all suggests that Trojan planets might be very commonly captured into orbits around Jovians – if they can avoid collision. As the stability mass-limit of a Trojan is something like 0.045 of the primary planet that might mean Trojans can be quite hefty… assuming not too much migration to stir things up.

Also the tidal heating history of a captured object can be pretty intense – Triton still has a melted surface of “negligable age” according the latest analysis, the result of cryotectonics presumably powered by tidal heating. Potentially that means a “habitable” exomoon where we wouldn’t expect one to exist. For a while in the 1970s Titan looked like, in some frequencies, it had a surface temperature close to the melting point of ice. Several models were developed of a nitrogen/hydrogen greenhouse effect to bring up the surface temperature. That’s not an unreasonable prospect for a tidally warmed exomoon around a Jupiter analogue.

Something I used to mention occasionally when I ventured here more often was the idea that you could start looking somewhat outside of the traditional habitable zone if you assumed you were looking for exo-moons which might stay quite warm as a result of tidal flexing.

So, if we’re gonna look for potentially life-hosting exo-moons, something I’ve been dreaming of for a decade or so, then we really do need to expand our definition of the traditional “habitable zone” or abandon it alltogether.

Abstract: We present a search for Trojan companions to 25 transiting exoplanets. We use the technique of Ford & Gaudi, in which a difference is sought between the observed transit time and the transit time that is calculated by fitting a two-body Keplerian orbit to the radial-velocity data. This technique is sensitive to the imbalance of mass at the L4/L5 points of the planet-star orbit.

No companions were detected above 2\sigma confidence. The median 2\sigma upper limit is 56 M_\earth, and the most constraining limit is 2.8 M_\earth for the case of GJ 436. A similar survey using forthcoming data from the Kepler satellite mission, along with the radial-velocity data that will be needed to confirm transit candidates, will be sensitive to 10-50 M_\earth Trojan companions in the habitable zones of their parent stars.

As a by-product of this study, we present empirical constraints on the eccentricities of the planetary orbits, including those which have previously been assumed to be circular. The limits on eccentricity are of interest for investigations of tidal circularization and for bounding possible systematic errors in the measured planetary radii and the predicted times of secondary eclipses.

Comments: Accepted for publication in The Astrophysical Journal (11 pages, in emulateapj format)

Charter

In Centauri Dreams, Paul Gilster looks at peer-reviewed research on deep space exploration, with an eye toward interstellar possibilities. For the last seven years, this site has coordinated its efforts with the Tau Zero Foundation, and now serves as the Foundation's news forum. In the logo above, the leftmost star is Alpha Centauri, a triple system closer than any other star, and a primary target for early interstellar probes. To its right is Beta Centauri (not a part of the Alpha Centauri system), with Beta, Gamma, Delta and Epsilon Crucis, stars in the Southern Cross, visible at the far right (image: Marco Lorenzi).

On Comments

Centauri Dreams publishes selected comments on the articles under discussion here. Among the criteria for selection: Comments must be on topic, directly related to the post in question, must use appropriate language and must not be abusive to others. Civility counts. In addition, a valid email address is required for a comment to be considered. Centauri Dreams is emphatically not a soapbox for political or religious views submitted by individuals or organizations.